Early efforts to incorporate GR effects in simulations
of accretion onto a BH indicated the likelihood of significant
outflow, even in purely HD situations
(Hawley et al. 1984).
However, until very recently, this work and other attempts along the
same lines were
greatly hampered by severe numerical difficulties. These demanded
the development of techniques, such as adaptive mesh refinement,
that allow one to efficiently and simultaneously compute flows in the
high density regions in the
accreting gas and in the low density expelled gas; following the
latter also requires much greater spatial scales which make the computations
extremely expensive.

Pioneering work on MHD launching of jets from disks was performed by
Uchida & Shibata
(1985),
who evolved an initially vertical magnetic field tied to a cold
thin disk rotating around a point mass assuming axisymmetry.
Differential rotation in the disk
produces a substantially toroidal field and this magnetic tension
is released through strong torsional Alfvén waves, which expel mass.
This approach has recently
been extended to 3-D relativistic flows around Schwarzschild BH's
by Koide et
al. (1998) and
Nishikawa et
al. (1999).
They find that a shock forms in the disk and yields a gas-pressure
driven jet which dominates the outflow, though a weaker MHD
jet is present outside the pressure driven jet.
In a truly impressive computation, this work has recently been
extended to the environs of a rapidly rotating Kerr BH
(Koide et al. 2000);
while the results for a corotating disk do not greatly differ from
those of the Schwarzschild situation, for (the relatively unlikely case of)
counter-rotating disks a very powerful magnetically driven jet is
formed inside the gas-pressure driven jet.

The launching of cold gas from a disk under circumstances carefully designed to
emulate the BP magneto-centrifugal mechanism has recently been simulated
in 3-D by
Krasnopolsky et
al. (1999).
If the field is set up to be
``propelling'' then rapid acceleration and collimation of the flow
are indeed observed. A simulation of the situation where a Keplerian
disk is initially threaded by a dipolar poloidal magnetic field has been
recently performed by
Ustyugova et
al. (2000);
they find that a quasi-stationary
collimated Poynting jet arises from the inner part of the disk, while
a steady uncollimated hydromagnetic outflow emerges from
the outer part of the disk. Although these calculations are
focussed on the types of overdense cooling jets that are to be found
in protostellar systems instead of AGN, it is also worth noting the
sophisticated numerical techniques involved in the simulations of
Stone & Hardee
(2000).

Early 2-D simulations of HD jets (e.g.,
Norman et al. 1982)
were of great importance in establishing
that extragalactic jets were of very low density and of high Mach number,
for the morphology of FR II radio galaxies could only be
reproduced under those circumstances. The jet is preceded by
a bow shock; the cocoon is comprised of shocked ambient medium,
separated by a contact discontinuity from jet material that has
passed through a Mach disk shock at the head of the jet, which
corresponds to the hot-spot. Since then, as the largest
computers have been turned to this task, the computations have
greatly improved in both spatial resolution and temporal duration.
Very long term 2-D simulations, which allowed the growth of
axisymmetric Kelvin-Helmholtz instabilities to go non-linear
(typically after the jets propagated distances corresponding to
hundreds of initial radii) indicated that
the lobes could become detached from the jets, but that new
Mach disks could form behind them, thereby explaining some of
the ``double-double'' radio source morphologies
(Hooda et al. 1994).
A suite of 2-D relativistic and nonrelativistic jets have
recently been compared to show that the velocity field of nonrelativistic
jet simulations cannot be scaled up to give the spatial
distribution of Lorentz factors seen in relativistic simulations,
as had been often speculated to be the case
(Rosen et al. 1999);
however, each relativistic jet and its nonrelativistic
equivalent do have similar ages, if expressed in the appropriate dynamical
time units.

Three-dimensional simulations have clearly shown that non-axisymmetric
instabilities will become important if even small perturbations are
applied (e.g.,
Hooda & Wiita 1998).
Nonetheless, the HD
jets can propagate to very substantial distances without completely
breaking up if they have high enough Mach numbers. A careful
comparison of numerical simulations and normal mode analysis for
relativistic 3-D jets has shown that a wide variety of helical modes
can be generated; these imply that dramatic variations in Doppler boosting
are possible without much overall bending of the jet
(Hardee 2000).
Higher resolution simulations of
relativistic jets indicate that the instabilities are greatly
reduced in comparison to nonrelativistic situations
(Aloy et al. 1999).
Other relativistic simulations have convincingly
shown that the knot structures seen
in VLBI observations can be reasonably reproduced in terms of shocks
within those jets (e.g.,
Martí et al. 1995,
Mioduszewksi et
al. 1997,
Gómez et
al. 1998).

The collision
of a jet with a much denser cloud have recently been reexamined using
high resolution 3-D HD simulations (e.g.,
Higgins et al. 1999,
Wang et al. 2000).
While powerful jets will destroy most obstructions and weak jets will
be stalled and destabilized by them (as probably happens in many Seyfert
galaxies), there is a rather small region
of parameter space where jets can bend and survive; this could
explain some rare ``dog-leg'' morphologies.

The instability of MHD jets, particularly focussed on the
question of entrainment, has been carefully studied under
various situations recently
(Hardee & Rosen
1999,
Rosen & Hardee
2000).
By precessing the jets at the origin to excite the KH
instability, results can be compared with linear stability analyses,
and it is concluded that the KH instability is the primary cause
for mass entrainment
but that expansion of the jet reduces the rate of mass entrainment.

An interesting approach to MHD jet stability has been taken by
Frank et al. (2000).
The initial conditions for the jets are taken from analytical
models for magneto-centrifugal launching and have a more complicated
structure than most earlier work. They find new behavior
including the separation of an inner jet
core from a low density collar. The wavelengths and growth rates
from a linear stability analysis are in good accord with
2.5 dimensional numerical simulations
(Lery & Frank 2000).
For a sub-class of current-driven instabilities in cold
supermagnetosonic jets, 3-D MHD simulations
have also found good agreement with a linear analysis
(Lery et al. 2000).
If the initial equilibrium structure has a pitch profile that
increases with radius, an
internal helical ribbon with a high current density forms,
which yields localized dissipation; this might produce
particle acceleration within the jet.